System and method for an efficient dynamic multi-unit auction

ABSTRACT

The present invention implements an auction in which multiple types of goods may be auctioned in a dynamic process. In a preferred embodiment, the present invention is a system and method for a computer implemented dynamic multi-unit auction in which the price paid or received by bidders tends to be independent of their own bids, in which participants may be provided with information concerning their competitors&#39; bids as the auction progresses, and in which the confidentiality of high values may be maintained. Participants&#39; quantities bid at a given time may be restricted to be less than or equal to the quantities bid at an earlier time. These features provide the advantage of improving economic efficiency of the auction design over the prior art.

[0001] RELATED APPLICATIONS

[0002] This application is a continuation-in-part of my priorapplication “System and Method for an Efficient Multi-Unit Auction,”Ser. No. 09/573,007, filed May 18, 2000.

[0003] This application is also related to prior applications Ser. Nos.60/216,338; 60/229,600; as well as Provisional Applications entitled“System and Method for an Efficient Dynamic Auction for Multiple Typesof Items,” filed May 29, 2001, bearing Ser. No. ______, and “System andMethod for an Efficient Dynamic Auction for Multiple Types of Items,”filed May 31, 2001, bearing Ser. No. ______. The disclosures of theforegoing applications are incorporated herein by this reference.

[0004] FIELD OF THE INVENTION

[0005] The present invention relates to improving computer-implementedauctions and, more particularly, to computer implementation of anefficient dynamic multi-unit auction.

BACKGROUND OF THE INVENTION

[0006] Auction formats in the art tend generally to be of the sealed-bidor ascending-bid variety. In the standard sealed-bid auction, bidders—inone single bidding round—simultaneously and independently submit bids tothe auctioneer, who then determines the auction outcome. In the standardascending-bid auction, bidders—in a dynamic bidding process—submit bidsin real time until no more bids are forthcoming. An ascending-bid formatoffers the advantage that there is feedback among participants' bids:each bidder is able to infer other bidders' information about the valueof the item(s) as the auction progresses and incorporate thisinformation into his subsequent bids. This feedback tends to result inmore efficient auction outcomes as well as in more aggressive bidding,resulting in higher expected revenues for the seller.

[0007] However, standard ascending-bid formats—such as the design usedby the Federal Communications Commission for auctioning radiocommunications spectrum—have the disadvantage that they do not generallylead to outcomes which are efficient in the sense of assigning items tothe bidders who value them the most. Most ascending-bid auction formatshave the unfortunate property that identical items sell at the uniformprice reached at the end of the auction. This creates incentives forbidders to engage in demand reduction: bidders have incentive tounderstate the values that they place on marginal units in order toreduce the market-clearing price (and, hence, the price they will pay onthe inframarginal units that they will win in any case). This has clearnegative implications both for efficiency and for revenues.

[0008] My prior patent, “System and Method for an Efficient DynamicAuction for Multiple Objects,” (U.S. Pat. No. 6,026,383, issued Feb. 15,2000) provides an early version of a system and method for acomputer-implemented dynamic auction, which may achieve efficiency forsituations involving multiple identical objects. The current inventionis an improved system and method for a computer-implemented dynamicauction, which improves upon the previous invention both in its efficacyof performance and in the generality of economic environments where itmay perform efficiently.

SUMMARY OF THE INVENTION

[0009] The present invention is a system and method for implementing ona computer a dynamic multi-unit auction in which the price paid orreceived by bidders tends to be independent of their own bids, in whichparticipants may be provided with information concerning theircompetitors' bids as the auction progresses, and in which theconfidentiality of high values is maintained. This provides theadvantage of improving the economic efficiency of the auction designover the prior art. The present invention usefully enables a seller orbuyer to efficiently auction multiple types of goods or services, and toefficiently auction items with complex possibilities for substitution.

[0010] The present invention is a computer or computer system thatreceives bids from a plurality of bidders for a plurality of items in adynamic bidding process and usually determines an allocation of theitems among bidders. The present invention is also acomputer-implemented method for receiving bids from a plurality ofbidders for a plurality of items in a dynamic bidding process andusually determining an allocation of the items among bidders. Thepresent invention is also a machine-readable medium having storedthereon data representing sequences of instructions, which when executedby a computer or computer system, cause said computer or computer systemto receive bids from a plurality of bidders for a plurality of items ina dynamic bidding process and usually to determine an allocation of theitems among bidders.

[0011] In one embodiment, the invention comprises a bidding informationprocessor (BIP) together with an auctioneer terminal (AT) and aplurality of bidder terminals (BT's) which communicate with the biddinginformation processor via a network. Bidders at the bidder terminalsenter bids in multiple rounds, and may observe displayed auctioninformation. The auctioneer at the auctioneer terminal controls theprogress of the auction. The BIP, the AT, and the BT's communicate andprocess information in order to conduct an auction.

[0012] Suppose that m (m≧1) types of items are being auctioned, and oneor more units of each type are being auctioned. An auction in accordancewith an embodiment of the present invention proceeds as follows. First,the auctioneer (i.e., the auctioneer terminal) establishes a pricevector, (P₁, . . . , P_(m)), which includes a price for each of the mtypes of items subject to the auction. The auctioneer communicates theprice vector to the auction computer (i.e., bidding informationprocessor), which in turn communicates it to bidders (i.e., bidderterminals). Second, plural bidders respond with bid vectors indicatingthe quantity of each respective type of item that the bidder wishes totransact at the current price vector. Let the bidders be superscriptedby i, where i=1, . . . , n. The quantity vector for bidder i is denotedby (Q₁ ^(I), . . . ,Q_(m) ^(I)). Also, let the quantities of therespective types of items being auctioned be denoted by({overscore(Q)}₁, . . . , {overscore (Q)}_(m)). The auction computer thendetermines, based on the received bids, whether the auction shouldcontinue. Typically, the starting price vector is selected such that theaggregate quantity of each type of item desired by all the bidders(i.e., Σ_(I=1) ^(n)Q_(k) ^(I)) is greater than the quantity of each typeof item being auctioned (i.e., {overscore (Q)}_(k)). In this event, theauction computer determines that the auction will continue, and eitherthe auction computer or the auctioneer will establish a revised pricevector (which is typically larger in each of its m components than theinitial price vector). The auction computer then sends to one or morebidders the revised price vector. Next, plural bidders respond with bidvectors indicating the quantity of each respective type of item that thebidder wishes to transact at the revised price vector. Again, typically,the aggregate quantity of each type of item desired by all the bidderswill not equal the available quantity, and a determination is again madethat the auction should continue. Nevertheless, one or more items of aparticular type may be credited with a particular bidder. The item(s),if any, will be credited at a price in a closed interval between theprice contained in the (previous) price vector and the price containedin the revised price vector. In one embodiment, items are credited atthe price contained in the revised price vector; in another embodiment,items are credited at the price contained in the (previous) pricevector; and in a third embodiment, items are credited at the average ofthe price contained in the revised price vector and the price containedin the (previous) price vector. In one preferred embodiment, thedetermination of whether a particular bidder is credited with a selectedtype of item is based on whether the sum of the bids of other bidders atthe revised price vector is different from the sum of the bids of otherbidders at the (previous) price vector. In this embodiment, if the twosums are different, the particular bidder is credited with a number ofthe selected type of items equal to the change in the sum of the bids ofother bidders. This process continues until a determination is made thatthe auction should not continue. In one preferred embodiment, after thedetermination to end the auction is made, the items are allocated tobidders according to their final bid vectors, and the payments ofbidders are based on the cumulative sequence of credits that occurredduring the course of the auction.

[0013] Certain constraints are desirable in order for this auction tooperate optimally and to reach an economically efficient outcome. Oneexemplary constraint is an activity rule which constrains a bidder notto increase his quantity, summed over the m types of items, from one bidin the auction to the next. Another exemplary constraint is a morestringent activity rule which constrains a bidder not to increase hisquantity, summed over a group of types of items, from one bid in theauction to the next. A third exemplary constraint is a more stringentactivity rule which constrains a bidder not to increase his quantity,individually on each of the m types of items, from one bid in theauction to the next. A fourth exemplary constraint is a reduction rulewhich constrains a bidder not to decrease his quantity, for any singletype of item, beyond the point where the sum of the quantities bid forthis type of item by all bidders equals the sum of the quantities beingauctioned. (If, in a given round, two or more bidders simultaneouslyattempt to decrease their quantities, for any single type of item,having the effect of reducing bids beyond the point where the sum of thequantities bid for this type of item by all bidders equals the sum ofthe quantities being auctioned, the auction procedure will resolve thisdiscrepancy. For example, the auctioneer may honor these attempts todecrease in order of time priority, or may ration these simultaneousattempts to decrease in proportion to the attempted reductions.)

[0014] While an auction following these rules could be conductedmanually, computerized conduct of the auction allows the auction to beconducted with all bidding information taken into account, whilecontrolling the degree to which the information itself is disclosed tothe participants. Computerized conduct of the auction also allows theauction to be conducted swiftly and reliably, even if bidders are notlocated on-site. The amount of information which is transmitted to thebidder terminals and/or actually displayed to the bidders may becarefully controlled. In one embodiment, all bidding information isdisplayed to the bidders. In another embodiment, no bidding informationis displayed to the bidders; only the results of the auction aredisplayed. A number of intermediate embodiments are also possible, inwhich some but not all bidding information is displayed to the bidders.For example, in one preferred embodiment, -the auctioneer disclose onlythe aggregate quantity bid for each type of item in each round, asopposed to disclosing each individual bid.

[0015] My prior patent U.S. Pat. No. 6,026,383 treats auctions formultiple, identical objects and close substitutes. The earlierapplication's efficient auction with one price clock exploited featuresof the homogeneous-good environment to construct an eminently-simpledynamic procedure. Unfortunately, the cases of multiple types of relateditems, or items with complex possibilities for substitution, do not lendthemselves to quite as simple a procedure. My other prior patents,“Computer Implemented Methods and Apparatus for Auctions,” U.S. Pat. No.5,905,975, issued May 18, 1999, and U.S. Pat. No. 6,021,398, issued Feb.1, 2000, describe other auction designs for multiple, dissimilar items.However, the current auction design appears likely in practice to besimpler and to run more swiftly, as well as placing lower computationaldemands on bidders.

[0016] The present invention extends my auction design described in U.S.Pat. No. 6,026,383 to treat-in a simple way-the case of auctioning a setof items which includes two (or more) items that are neither identicalnor perfect substitutes to one another, so that two or more price clocksare required. Henceforth, this will be described for short as asituation with “multiple types of multiple items,” or simply“heterogeneous items” or “heterogeneous objects.” Often, but not always,the heterogeneous items auctioned together will bear some relationshipto one another: for example, they may be licenses or rights to performessentially the same activity at different geographic locations; or theymay be securities issued by the same entity but with different durationsto maturity; or they may be related goods with slightly differentcharacteristics that render them only imperfect substitutes.

[0017] The present invention may also be better suited than previousauction designs for treating the case of identical objects or perfectsubstitutes which exhibit “increasing returns” for bidders. “Increasingreturns” refers to a situation where the extra value that a bidderderives from an (N+1)^(st) unit is greater than the extra value that abidder derives from an N^(th) unit. For example, this would include asituation where the utility from two units is strictly more than doublethe utility derived from one unit.

[0018] The present invention is useful for conducting auctions involvingitems offered for sale by the bidders, as well as items offered for saleto the bidders. Although terms such as “vector of quantities demanded”(by a bidder) and “demand curve” (of a bidder) are used to describe thepresent invention, the terms “vector of quantities offered” (by abidder) and “supply curve” (of a bidder) are equally applicable. In somecases, this is made explicit by the use of both terms, or by the use ofthe terms “vector of quantities transacted” (by a bidder) and“transaction curve” (of a bidder). The term “quantities transacted”includes both “quantities demanded” and “quantities offered”. The term“bid” includes both offers to sell and offers to buy. The term“transaction curve” includes both “demand curve” and “supply curve”.Moreover, any references to “quantities being offered” includes both“quantities being sold” by the auctioneer, in the case this is anauction for selling items, as well as “quantities being bought orprocured” by the auctioneer, in the case this is an auction for buyingitems or procuring items.

[0019] Moreover, while standard auctions to sell typically involveascending prices, the present invention may utilize prices that ascendand/or descend. One useful situation in which the price would be allowedto descend is a procurement auction or “reverse auction,” an auction tobuy.

[0020] Throughout this document, the terms “objects”, “items”, “units”and “goods” are used essentially interchangeably. The inventive systemmay be used both for tangible objects, such as real or personalproperty, and intangible items, such as telecommunications licenses orelectric power. The inventive system may be used in auctions where theauctioneer is a seller, buyer or broker, the bidders are buyers, sellersor brokers, and for auction-like activities which cannot be interpretedas selling or buying. The inventive system may be used for itemsincluding, but not restricted to, the following: public-sector bonds,bills, notes, stocks, and other securities or derivatives;private-sector bonds, bills, notes, stocks, and other securities orderivatives; communication licenses and spectrum rights; clearing,relocation or other rights concerning encumbrances of spectrum licenses;electric power and other commodity items; rights for terminal, entry,exit or transmission capacities or other rights in gas pipeline systems;airport landing rights; emission allowances and pollution permits; andother goods, services, objects, items or other property, tangible orintangible. It may also be used for option contracts on any of theabove. It may be used in initial public offerings, secondary offerings,and in secondary or resale markets.

[0021] The network used, if any, can be any system capable of providingthe necessary communication to/from BIP, BT, and AT. The network may bea local or wide area network such as, for example, ethernet, token ring,the Internet, the World Wide Web, the information superhighway, anintranet or a virtual private network, or alternatively a telephonesystem, either private or public, a facsimile system, an electronic mailsystem, or a wireless communications system.

BRIEF DESCRIPTION OF THE DRAWINGS

[0022]FIG. 1 is a graphical depiction of the architecture of anexemplary client-server computer system in accordance with an embodimentof the invention;

[0023]FIG. 2 is another graphical depiction of an exemplary computersystem in accordance with an embodiment of the invention;

[0024]FIG. 3 is a detail of one element of the computer system of FIG.2;

[0025]FIG. 4 is a flow diagram of an auction process in accordance withone embodiment of the invention;

[0026]FIG. 5 is a more detailed flow diagram illustrating, in moredetail, an element of the diagram of FIG. 4;

[0027]FIGS. 6a and 6 b are more detailed flow diagrams illustrating, inmore detail, elements of the diagram of FIG. 4;

[0028]FIG. 7 is a more detailed flow diagram illustrating, in moredetail, an element of the diagram of FIG. 4;

[0029]FIG. 8 is a more detailed flow diagram illustrating, in moredetail, an element of the diagram of FIG. 4; and

[0030]FIGS. 9a, 9 b and 9 c are more detailed flow diagramsillustrating, in more detail, elements of the diagram of FIG. 4.

[0031] DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0032] The drawings of FIGS. 1-4 of my prior patent U.S. Pat. No.6,026,383 and of FIGS. 1-12 of my prior patent U.S. Pat. No. 5,905,975,and the associated text of each, provide a general superstructure forthe present auction method and system, especially as it relates to thecomputer implementation thereof. Moreover, the terminology establishedin the previous applications will be relied upon as needed. Thefollowing description will detail the flow of the novel features of thepreferred embodiments of the present method and system for an efficientdynamic multi-unit auction.

[0033] Before describing the auction process in detail, reference ismade to FIG. 1 to describe the architecture of an exemplary computersystem in accordance with an embodiment of the present invention. In thegraphical depiction of FIG. 1, the computer system consists of multipleclients 20 a-n and 30 communicating with the server 10 over a network40. The clients 20 a-n are the bidders, the client 30 is the auctioneer,and the server 10 is the auction computer. The server 10 consists of aCPU 11, memory 12, a data storage device 13, a communications interface14, a clock 15, an operating system 16, and an auction program 17.

[0034]FIG. 2 is another graphical depiction of an exemplary computersystem in accordance with an embodiment of the present invention. Theauction system of FIG. 2 includes an auction computer 60 (sometimes alsoreferred to as a Bidding Information Processor or BIP), a plurality ofuser systems 70 a, 70 b and so on (sometimes also referred to as BidderTerminal or BT), each user system 70 a-n representing an individualbidder, and a user system 80 (sometimes also referred to as anAuctioneer Terminal or AT). The systems 60, 70 a-n, and 80 communicateover a network 90. The network represents any system capable ofproviding the necessary communication to/from BIP, BT, and AT. Thenetwork may be a local or wide area network such as, for example,ethernet, token ring, the Internet, the World Wide Web, the informationsuperhighway, an intranet or a virtual private network, or alternativelya telephone system, either private or public, a facsimile system, anelectronic mail system, or a wireless communications system. Each of thesystems 60, 70 a-n, and 80 may include a typical user interface 65, 75a-n, 85 for input/output which may include a conventional keyboard,display, and other input/output devices. Within each of the systems, theuser interface (65, 75 a-n, 85) is coupled to a network interface (64,74 a-n, 84), which in turn communicates via the network 90. Both theuser interface and network interface connect, at each system, to a CPU(62, 72 a-n, 82). Each system includes a memory (66, 76 a-n, 86). TheBIP 60 also includes a clock 61 and a data storage device 63, which willordinarily contain a database. (However, in some embodiments thedatabase might instead be stored in memory 66.) The memory 66 of the BIP60 can further be broken down into a program 67, data 68 and anoperating system 69. The memory (76 a-n, 86) of the BT's 70 a-n and theAT 80 may include a web browser (for example, Internet Explorer orNetscape) (79, 89) or other general-purpose software, but notnecessarily any computer program specific to the auction process. Ineach system the CPU (62, 72 a-n, 82) represents a source of intelligencewhen executing instructions from the memory (66, 76 a-n, 86) so thatappropriate input/output operations via the user interface and thenetwork interface take place as is conventional in the art. Theparticular steps used in implementing the inventive auction system aredescribed in more detail below. In one embodiment, each of the systemsare personal computers or workstations.

[0035]FIG. 3 is a more detailed illustration of an exemplary BIP 60showing details of the database. As discussed for FIG. 2, the databaseis ordinarily stored on a data storage device 63, although in someembodiments it might instead be stored in memory 66. As depicted in FIG.3, the database includes provision for creating, storing, and retrievingrecords representing Items in the Auction 63-1, Status of the Items inthe Auction 63-2, Auction Schedule 63-3, Current Price(s) 63-4, List ofBidder ID's 63-5, List of Passwords 63-6, Bidding History 63-7, andConstraints on Bids 63-8. The particular set of data required for anyparticular auction and the format of that datum or data (such as scalar,vector, list, etc.) is more particularly specified by the detaileddescription of that auction.

[0036] Embodiments Concerned with Heterogeneous Commodities

[0037] Many of the most useful embodiments of the present inventionapply in situations where an entity wishes to sell or buy heterogeneousitems or commodities. A type of item is defined so that two units of thesame type are identical items or close substitutes, while two units ofdifferent types exhibit significant differences in time, location or anyother product characteristics. Typically, there are multiple units ofeach type of item. Items or commodities are defined to be heterogeneouswhen there are two or more types of items.

[0038] The various embodiments of the present invention tend to be themost useful when the items are heterogeneous (so that the system andmethod for a dynamic auction of homogeneous commodities, described inU.S. Pat. No. 6,026,383, does not apply), but nevertheless there is someconnection or relation between the different types of items (so thatthere is good reason to sell or buy the different types of commoditiesin a single auction process). Examples of heterogeneous items for whichthere may be significant commercial possibilities for embodiments of thepresent invention include the following:

[0039] Treasury bonds or other securities: For example, a government orcentral bank may wish to auction 3-month, 6-month and 12-month Treasurysecurities together. Thus, there are three types of heterogeneous items.

[0040] Electricity contracts: An electric generating company may wish tosimultaneously auction some forward contracts or options contracts forbase-load and peak-load electricity generation, with durations of 2months, 3 months, 6 months, 12 months, 24 months and 36 months,respectively. Thus, there are 2×6=12 types of heterogeneous commodities.

[0041] Entry capacity into a gas pipeline system: A gas pipeline companywishes to simultaneously auction the capacity to enter the gas pipelinesystem at five geographically-dispersed terminals. Thus, there are fivetypes of heterogeneous commodities.

[0042] Two or more heterogeneous consumer commodities (e.g., oranges andgrapefruits).

[0043] In what follows, we will assume that m (m≧1) types of items arebeing auctioned, and that there are n (n≧1) bidders participating in theauction. An auction in accordance with an embodiment of the presentinvention proceeds as follows. First, the auctioneer (i.e., theauctioneer terminal) determines a starting price vector, (P₁, . . .,P_(m)), and transmits it to the bidding information processor, which inturn transmits it to bidders (i.e., bidder terminals). Second, a bidderresponds with a bid vector indicating the quantity of each respectivetype of item that the bidder wishes to transact at the current pricevector. Let the bidders be superscripted by i, where (i=1, . . . , n)The bid vector for bidder i is denoted by (Q₁ ^(I), . . . ,Q_(m) ^(I)).The following definitions are helpful in describing the processassociated with a first embodiment of the present invention.

[0044] DEFINITIONS.

[0045] The available quantities ({overscore (Q)}₁, . . . , {overscore(Q)}_(m)) refer, in the case of an auction to sell, to the quantities ofthe m respective types of items offered to be sold in the auction or, inthe case of an auction to buy (i.e., a procurement auction or a “reverseauction”), to the quantities of the m respective types of items offeredto be bought in the auction. Optionally, the available quantities may beallowed to depend on the prices, or otherwise be contingent on theprogress of the auction.

[0046] The current prices comprise a vector, (P₁, . . . ,P_(m)), whosecomponents represent the prices for the m respective types of items.

[0047] The current bid of bidder i comprises a vector, (Q₁ ^(I), . . .,Q_(m) ^(I)), whose components represent the quantities that bidder i iswilling to buy (in the case of an auction to sell) or to sell (in thecase of an auction to buy) at the current prices for the m respectivetypes of items.

[0048] The current bids comprise the collection of vectors, {Q₁ ^(I), .. . ,Q_(m) ^(I)}_(I=1) ^(n), consisting of the current bid of bidder ifor every bidder (i=1, . . . , n) in the auction.

[0049] The bidding history comprises the current prices and the currentbids associated with the present time and all earlier times in thecurrent auction.

[0050] A clock auction is a dynamic auction procedure whereby: theauctioneer announces the current prices to bidders; the bidders respondwith current bids; the auctioneer determines whether the auction shouldcontinue based on the bidding history; the auctioneer updates thecurrent prices based on the bidding history and the process repeats, ifit is determined that the auction should continue; and the auctioneerallocates the items among the bidders and assesses payments among thebidders based on the bidding history, if it is determined that theauction should not continue.

[0051] Observe that a “clock auction” differs from a standardascending-bid electronic auction in the following important sense. Instandard ascending-bid electronic auctions—such as in the FederalCommunications Commission auctions for radio communications spectrum orin eBay Auctions—the bidders name prices (and, perhaps also, quantities)that they propose to pay for the items being auctioned, in an iterativeprocess. In a standard clock auction, the auctioneer sets the pace forprice increases, and bidders respond only with quantities in aniterative process. (However, in the discussion of Intra-Round Bids,below, it will be seen that there still may be a role for bidders namingprices—to a limited extent—in a clock auction.)

[0052]FIG. 4 is a flow diagram of a clock auction in accordance with oneembodiment of the present invention. The process starts with step 102,in which memory locations of a computer are initialized. In onepreferred embodiment, the appropriate memory locations of the biddinginformation processor (auction computer) are initialized withinformation such as the items in the auction, the available quantity ofeach type of item in the auction, the initial price vector, the auctionschedule, a list of bidder ID's, and a list of passwords. In step 104, acomputer outputs auction information, including the starting pricevector (P₁, . . . ,P_(m)). In one preferred embodiment, the biddinginformation processor outputs the auction information through itsnetwork interface and transmits it via the network. The bidder terminalsthen receive the auction information through their network interfacesand display the information to bidders through their user interfaces. Instep 106, a computer receives bids (Q₁ ^(I), . . . ,Q_(m) ^(i)) frombidders. In one preferred embodiment, a bidder inputs his bids throughthe user interface of the bidder terminal, which then outputs theauction information through its network interface and transmits it viathe network. The bidding information processor then receives the bidsthrough its network interface for use in the next step. In step 108, acomputer applies constraints, if any, to the received bids, and entersonly those bids that satisfy said constraints. This process isillustrated in greater detail in FIGS. 6a and 6 b. In one preferredembodiment, the constraints are applied at the bidding informationprocessor, although they may also easily be applied at the bidderterminals. In step 110, a computer calculates changes, if any, tobidders' payment accounts, based on the entered bids. This process isshown in more detail in FIG. 5. In one preferred embodiment, the changesto bidders' payment accounts are calculated at the bidding informationprocessor. In step 112, a computer determines whether the auction shouldcontinue. An exemplary process of step 112 is illustrated in greaterdetail in FIGS. 7. In one preferred embodiment, this determinationoccurs at the bidding information processor.

[0053] If the auction should continue, the process goes to step 114, inwhich a computer updates the price vector (P₁, . . . ,P_(m)), and step116, in which a computer updates other auction information, if any. Anexemplary process of step 114 is illustrated in greater detail in FIG.8. In one preferred embodiment, the bidding information processorautomatically generates a suggested revised price vector, outputs thesuggested revised price vector through its network interface, andtransmits it via the network. The auctioneer terminal then receives thesuggested revised price vector through its network interface anddisplays it to the auctioneer through its user interface. The auctioneereither approves or modifies the revised price vector through the userinterface of the auctioneer terminal, which then outputs the revisedprice vector through its network interface and transmits it via thenetwork. The bidding information processor then receives the revisedprice vector through its network interface for use in subsequent steps.The process then loops to step 104.

[0054] If the auction should not continue, the process goes to step 118,in which a computer outputs a final message, including the allocation ofitems among bidders and the payments of the bidders. In one preferredembodiment, the bidding information processor takes the allocation ofitems among bidders to be their final bids and takes the payments of thebidders to be the final amounts in their payment accounts, and outputsthe allocation and payment outcome through its network interface andtransmits it via the network. The bidder terminals and auctioneerterminal then receive the allocation and payment outcome through theirnetwork interfaces and display the information to bidders and theauctioneer through their user interfaces. The process then ends.

[0055] Embodiments Concerned with an Efficient Dynamic Auction forHeterogeneous Commodities

[0056]FIG. 5 is a flow diagram of the subprocess of step 110 in which acomputer calculates changes, if any, to bidders' payment accounts. Theembodiment of the present invention shown in FIG. 5 makes bidders'payments as independent as possible of their own bids, and so a bidderhas little incentive to manipulate the auction process even if thebidder possesses market power. An auction that utilizes the process ofFIG. 5 will henceforth be referred to as the “Efficient Dynamic Auctionfor Heterogeneous Commodities.”

[0057] While the theoretical properties of the Efficient Dynamic Auctionfor Heterogeneous Commodities are not yet fully developed, and I do notwish to be bound by the result that I now state, it is helpful inpondering its usefulness to consider the following remarkable result,which I have proved elsewhere:

[0058] THEOREM. Suppose that bidders have purely private values for thecommodities in the auction, and suppose that their utility functions areconcave in the commodities and quasilinear in money. For any initialprice vector and for any initial value in bidders' payment accounts:

[0059] (i) sincere bidding by every bidder is a subgame perfectequilibrium of the Efficient Dynamic Auction for HeterogeneousCommodities; and

[0060] (ii) with sincere bidding, the price vector converges to aWalrasian equilibrium price, and hence the allocation of commoditiesattains full economic efficiency.

[0061] Unlike auction procedures in the prior art, the present inventionwill tend to yield fully-efficient outcomes, if bidders bid optimally.

[0062] While the previous and following description of the EfficientDynamic Auction for Heterogeneous Commodities is framed largely in termsof regular auctions to sell (where bidders are buyers), the invention isequally applicable for reverse or procurement auctions to buy (wherebidders are sellers). For the sake of brevity, this specification willnot run through the process a second time with the roles of selling andbuying reversed, but it should be clear to anybody skilled in the artthat the technology can be equally used in both situations.

[0063]FIG. 5 is a flow diagram of a subprocess of step 110. It beginswith step 110-1, in which a bidder i who has not yet been considered isselected. In step 110-2, a “payment-account-calculation indicator” forbidder i is examined. This indicator is set equal to 1 if changes tobidder i's payment account are supposed to be calculated at this step ofthe auction; and this indicator is set equal to 0, otherwise. In thepreferred embodiment of the present invention that yields the theoremstated above, this indicator is always set equal to 1 (and so the steps110-3 and 110-4 are always performed). However, in other embodiments ofthe present invention, the payment-account-calculation indicator isinitially set equal to 0 and is changed to 1 only when specific criteriaare satisfied, or never at all.

[0064] If the payment-account-calculation index is already equal to 1,the process goes to step 110-3. In step 110-3, for each k=1, . . . , m,a computer calculates:$\Delta_{k}^{i,t} = {\sum\limits_{j \neq i}\left( {Q_{k}^{j,t} - Q_{k}^{j,{t - 1}}} \right)}$

[0065] That is, Δ_(k) ^(I,t) is the change in the aggregate demands ofbidder i's opponents for items of type k, between the previous bids andthe current bids. Δ_(k) ^(I,t) is calculated as follows: for each type kof item in the auction and for each opposing bidder j≠i, the computertakes the difference between bidder j's demand at time t for items oftype k and bidder j's demand at time t−1 for items of type k. Summingthis, over all opposing bidders j≠i, yields Δ_(k) ^(I,t).

[0066] The process then proceeds to step 110-4, in which the paymentaccount value for bidder i is updated. In the preferred embodiment ofthe present invention that yields the theorem stated above, the paymentaccount value for bidder i can initially be set to any arbitraryconstant. One initial value that has desirable theoretical propertiesis:${\sum\limits_{k = 1}^{m}\quad {P_{k}^{0}\left( {{\overset{\_}{Q}}_{k} - {\sum\limits_{j \neq i}Q_{k}^{j,0}}} \right)}},$

[0067] where P_(k) ⁰ denotes the initial price for the commodity of typek, and Q_(k) ^(j,0) is opposing bidder j's initial demand for thecommodity of type k. After the initial time that step 110-4 is executedfor bidder i, the previous payment account value, denoted A^(I,t−)1, isrecalled. An updated payment account value, denoted A^(I,t), is computedby the following equation:$A^{i,t} = {A^{i,{t - 1}} - {\sum\limits_{k = 1}^{m}\quad {\Delta_{k}^{i,t}{P_{k}^{t}.}}}}$

[0068] This equation for updating the payment account value has thefollowing interpretation: bidder i is credited with the quantity −Δ_(k)^(I,t) of items of type k. Effectively, every time bidder i's opponentschange their aggregate quantity demanded by −Δ_(k) ^(I,t) units, theauction process implicitly assumes that −Δ_(k) ^(I,t) units will beawarded to bidder i, and the auction process charges bidder i thecurrent price vector of P_(k) ^(t) for each of these units. (Moreover,if ever bidder i's opponents increase their aggregate quantity demanded,so that Δ_(k) ^(I,t) is a positive number, then bidder i is debited withthe quantity Δ_(k) ^(I,t) of items of type k. The auction processimplicitly then assumes that Δ_(k) ^(I,t) units will be taken away frombidder i, and the auction process pays bidder i the current price vectorof P_(k) ^(t) for each of these units.) It is not necessary thatliterally the current price vector, P_(k) ^(t), is used in step 110-4.In other embodiments, the previous price vector, P_(k) ^(t−1), or someprice in the interval between P_(k) ^(t−1) and P_(k) ^(t) is used. Theprocess then proceeds to step 110-5, where it is determined whether allbidders have been considered. If not, the process loops back to step110-1. If all bidders have been considered, the process goes to step 112of FIG. 4.

[0069] If the payment-account-calculation indicator for bidder i is notequal to 1, the process goes to step 110-6. In step 110-6, it isdetermined whether the payment-account-calculation indicator should beset equal to 1. As stated earlier, in the preferred embodiment of thepresent invention that yields the theorem stated above, this step isnever reached, as the indicator is always set equal to 1. However,another exemplary embodiment of the present invention would only havethe indicator set equal to 1 for bidder i when the aggregate demand ofbidder i's opponents drops to less than the available quantity. Yetanother exemplary embodiment of the present invention would only havethe indicator set equal to 1 when the aggregate demand of all biddersdrops to less than a predetermined percentage of the available quantity,for example when the aggregate demand of all bidders first becomes lessthan 120% of the available quantity.

[0070] If the payment-account-calculation indicator for bidder i shouldbe set equal to 1, the process goes to step 110-7, where the indicatorfor bidder i is set equal to 1. The process then continues with steps110-3 and 110-4, where changes to bidder i's payment account value arecalculated. If the payment-account-calculation indicator for bidder ishould not be set equal to 1, the process loops directly to step 110-5without changing the payment account value for bidder i.

[0071] It is useful for understanding the Efficient Dynamic Auction forHeterogeneous Commodities to, at this point, work through an example ofthe auction process where there are two types of items (i.e., m=2).Real-world examples fitting this description may include the sale ofthree-month and six-month Treasury bills, or the sale of base-load andpeak-load electricity. However, we will generically refer to them ascommodity A and commodity B. Suppose that the supply vector is (10,8),i.e., commodities A and B are available in supplies of 10 and 8,respectively, and suppose that there are n=3 bidders. The auctioneerinitially announces a price vector of p₁=(3,4), and subsequently adjuststhe price vector to P₂=(4,5), p₃=(5,7), p₄=(6,7), and finally p₅=(7,8).The bidders' reports of quantities demanded at these price vectors areshown in Table 1: TABLE 1 Price and Quantity Vectors for IllustrativeExample with m = 2 Price Vector Bidder 1 Bidder 2 Bidder 3 p₁ = (3,4)(5,4) (5,4) (5,4) p₂ = (4,5) (4,4) (5,4) (4,3) p₃ = (5,7) (4,3) (4,4)(4,1) p₄ = (6,7) (4,3) (4,4) (3,2) p₅ = (7,8) (4,2) (3,4) (3,2)

[0072] The crediting of units to bidders occurs as follows. First,consider Bidder 1. When the price vector advances from p₁=(3,4) top₂=(4,5), the sum of the quantity vectors demanded by Bidder 1'sopponents decreases from (10,8) to (9,7). Thus, 1 unit of commodity Aand 1 unit of commodity B can be thought of as becoming available toBidder 1 at the current price of P₂=(4,5). The auction algorithm takesthis literally, by crediting 1 unit of commodity A at a price of 4, and1 unit of commodity B at a price of 5, to Bidder 1. Next, considerBidder 2. When the price vector advances from p₁=(3,4) to p₂=(4,5), thesum of the quantity vectors demanded by Bidder 2's opponents decreasesfrom (10,8) to (8,7). Thus, 2 units of commodity A and 1 unit ofcommodity B can be thought of as becoming available to Bidder 2 at thecurrent price. The auction algorithm takes this literally, by crediting2 units of commodity A at a price of 4, and 1 unit of commodity B at aprice of 5, to Bidder 2. Finally, consider Bidder 3. When the pricevector advances from p₁=(3,4) to P₂=(4,5), the sum of the quantityvectors demanded by Bidder 3's opponents decreases from (10,8) to (9,8).Thus, 1 unit of commodity A and 0 units of commodity B can be thought ofas becoming available to Bidder 3 at the current price. Again, theauction algorithm takes this literally, by crediting 1 unit of commodityA at a price of 4, and 0 units of commodity B at a price of 5, to Bidder3.

[0073] The process continues as the price vector advances. Oneinteresting moment occurs when the price advances from p₃=(5,7) top₄=(6,7). Observe that Bidder 3's demand vector changes from (4,1) to(3,2), while the other bidders' demand vectors remain constant. Inparticular, Bidder 3's demand for commodity B increases, meaning that 1fewer unit of commodity B remains available for Bidders 1 and 2.Consequently, the auction algorithm needs to take this literally, bydebiting 1 unit of commodity B at the current price of 7 from each ofBidders 2 and 3.

[0074] The entire progression of units credited and debited-and theassociated progression of changes to the bidders' payment accounts-issummarized for this example in Table 2: TABLE 2 Credits and Debits forIllustrative Example with m = 2 Price Vector Bidder 1 Bidder 2 Bidder 3P₁ = Initialization Initialization Initialization (3,4) P₂ = 1 unit of Acredited 2 units of A credited 1 unit of A credited (4,5) at 4 at 4 at 41 unit of B credited 1 unit of B credited 0 units of B credited at 5 at5 at 5 Cumulative Cumulative Cumulative payment = 9 payment = 13 payment= 4 P₃ = 1 unit of A credited 0 units of A credited 1 unit of A credited(5,7) at 5 at 5 at 5 2 units of B credited 3 units of B credited 1 unitof B credited at 7 at 7 at 7 Cumulative Cumulative Cumulative payment =28 payment = 34 payment = 16 P₄ = 1 unit of A credited 1 unit of Acredited 0 units of A credited (6,7) at 6 at 6 at 6 1 unit of B debited1 unit of B debited 0 units of B credited at 7 at 7 at 7 CumulativeCumulative Cumulative payment = 27 payment = 33 payment = 16 P₅ = 1 unitof A credited 0 units of A credited 1 unit of A credited (7,8) at 7 at 7at 7 0 units of B credited 1 unit of B credited 1 unit of B credited at8 at 8 at 8 Cumulative Cumulative Cumulative payment = 34 payment = 41payment = 31

[0075] At p₅=(7,8), supply and demand are now in balance for bothcommodities. Thus, p₅ becomes the final price. Bidders 1, 2 and 3 areallocated the quantity vectors of (4,2), (3,4) and (3,2), respectively,that they demanded at the final price. In addition, Bidders 1, 2 and 3are charged payments of 34, 41 and 31, respectively, the amounts accruedin their payment accounts at the end of the auction. Since many of thecredits and debits in the sequence occurred at earlier prices, bidders'payments do not generally equal their final quantity vectors evaluatedat the final prices. Rather, if the procedure described above isperformed along a continuous price path, the bidders' payments arerelated to those derived from a Vickrey auction (also known as aVickrey-Clarke-Groves mechanism). I develop this result elsewhere.

[0076] Embodiments of the Invention Concerned with Applying Constraintsto Bids

[0077]FIGS. 6a and 6 b are flow diagrams of two exemplary subprocessesof step 108. The process of FIG. 6a begins with step 108 a-1, in which abidder i who has not yet been considered is selected. In step 108 a-2, abid (Q_(k) ^(I,t))_(kεG) by bidder i which has not yet been consideredis selected. G is defined to be a group of item types. G is a nonemptysubset of {1, . . . , m}, the set of all item types. In step 108 a-3, itis checked whether each quantity Q_(k) ^(I,t) in the selected bid is anonnegative integer. If each component of the bid is a nonnegativeinteger, the process goes to step 108 a-4. In step 108 a-4, it ischecked whether the selected bid is consistent with bidder i's initialeligibility, that is, whether:${{\sum\limits_{k \in G}Q_{k}^{i,t}} \leq {\overset{\_}{Q}}_{G}^{i}},$

[0078] where bidder i's initial eligibility, {overscore (Q)}_(G) ^(I),for group G may, for example, be determined by the level of financialguarantee posted by bidder i. If the selected bid is consistent withbidder i's initial eligibility, the process goes to step 108 a-5, wherebidder i's most recent previously-processed bid for group G, denoted(Q_(k) ^(I,t−1))_(kεG), is recalled. In step 108 a-6, it is checkedwhether the selected bid is consistent with the auction's activity rule,that is, whether the constraint:${{\sum\limits_{k \in G}Q_{k}^{i,t}} \leq {\sum\limits_{k \in G}Q_{k}^{i,{t - 1}}}},$

[0079] is satisfied. If it is, the process continues to step 108 a-7,where the selected bid (Q_(k) ^(I,t))_(kεG) is entered as a valid bid bybidder i on group G. Optionally, bidder i is sent a message confirmingto him that the bid is valid. The process then goes to step 108 a-8,where it is determined whether all bids by bidder i have beenconsidered. If not, the process loops back to step 108 a-2. If all bidsby bidder i have been considered, the process continues to step 108 a-9,where it is determined whether all bidders have been considered. If not,the process loops back to step 108 a-1. If all bidders have beenconsidered, the process goes to step 110 of FIG. 4.

[0080] If the selected bid fails any of the checks at steps 108 a-3, 108a-4 or 108 a-6, the process instead goes to step 108 a-10, where amessage is outputted to bidder i that the selected bid is invalid. Theselected bid then is not entered as a valid bid. The process then goesto step 108 a-8, where it is determined whether all bids by bidder ihave been considered. If not, the process loops back to step 108 a-2. Ifall bids by bidder i have been considered, the process continues to step108 a-9, where it is determined whether all bidders have beenconsidered. If not, the process loops back to step 108 a-1. If allbidders have been considered, the process goes to step 110 of FIG. 4.

[0081] The process of FIG. 6b begins with step 108 b-1, in which abidder i who has not yet been considered is selected. In step 108 b-2, abid (Q_(k) ^(I,t))_(kεG) by bidder i which has not yet been consideredis selected. In step 108 b-3, it is checked whether each quantity Q_(k)^(I,t) in the selected bid satisfies the constraint:${{\sum\limits_{k \in G}{C_{k}^{i,t}Q_{k}^{i,t}}} \leq {\overset{\_}{C}}_{G}^{i,t}},$

[0082] where C_(k) ^(I,t) and {overscore (C)}_(G) ^(I,t) are arbitraryconstants. If the constraint of step 108 b-3 is satisfied, the processgoes to step 108 b-4. In step 108 b-4, it is checked whether eachquantity Q_(k) ^(I,t) in the selected bid satisfies the constraint:${{\sum\limits_{k \in G}{C_{k}^{{\prime i},t}Q_{k}^{i,t}}} \geq {\hat{C}}_{G}^{i,t}},$

[0083] where C′_(k) ^(I,t) and Ĉ_(G) ^(I,t) are arbitrary constants. Ifthe constraint of step 108 b-4 is satisfied, the process goes to step108 b-5, where it is checked whether the selected bid was submitted at atime no earlier than the starting time of the current round. If it was,the process goes to step 108 b-6, where it is checked whether theselected bid was submitted at a time no later than the ending time ofthe current round. If it was, the process continues to step 108 b-7,where the selected bid (Q_(k) ^(I,t))_(kεG) is entered as a valid bid bybidder i on group G. Optionally, bidder i is sent a message confirmingto him that the bid is valid. The process then goes to step 108 b-8,where it is determined whether all bids by bidder i have beenconsidered. If not, the process loops back to step 108 b-2. If all bidsby bidder i have been considered, the process continues to step 108 b-9,where it is determined whether all bidders have been considered. If not,the process loops back to step 108 b-1. If all bidders have beenconsidered, the process goes to step 110 of FIG. 4.

[0084] If the selected bid fails any of the checks at steps 108 b-3, 108b-4, 108 b-5 or 108 b-6, the process instead goes to step 108 b-10,where a message is outputted to bidder i that the selected bid isinvalid. The selected bid then is not entered as a valid bid. Theprocess then goes to step 108 b-8, where it is determined whether allbids by bidder i have been considered. If not, the process loops back tostep 108 b-2. If all bids by bidder i have been considered, the processcontinues to step 108 b-9, where it is determined whether all biddershave been considered. If not, the process loops back to step 108 b-1. Ifall bidders have been considered, the process goes to step 110 of FIG.4.

[0085] Embodiments Concerned with Continuing the Auction and PriceAdjustments

[0086]FIG. 7 is a flow diagram of a subprocess of step 112 of FIG. 4. Itillustrates an exemplary process by which a computer may determinewhether the auction should continue. (Related to this will also be FIG.9b, below, which illustrates an exemplary process by which a computerdetermines whether the auction should continue, in a system wherebidders are permitted to submit Intra-Round Bids.) FIG. 7 begins withstep 112 a-1, in which an item type k not yet considered is selected. Instep 112 a-2, a computer determines whether the aggregate quantity bidfor item type k is within {overscore (C)}_(k) of the available quantity,that is, whether:${{{- {\overset{\_}{Q}}_{k}} + {\sum\limits_{i = 1}^{n}Q_{k}^{i}}}} \leq {{\overset{\_}{C}}_{k}.}$

[0087] The constant, {overscore (C)}_(k), has the interpretation thatthis is the tolerance to which the auctioneer is allowing oversell orundersell to occur. If the auctioneer needs to sell exactly theavailable quantity of item type k, then {overscore (C)}_(k)=0. If thisinequality is not satisfied, then item type k has not yet cleared, andso the auction should continue. The process thus jumps immediately tostep 114 of FIG. 4.

[0088] If the inequality of step 112 a-2 is satisfied, the process thengoes to step 112 a-3, where it is determined whether all item types khave been considered. If not, the process loops back to step 112 a-1.However, if all item types k have already been considered, then it hasbeen found that all item types k have cleared within a tolerance of{overscore (C)}_(k), and so the auction should not continue. The processproceeds to step 118 of FIG. 4, where the final message is generated.

[0089]FIG. 8 is a flow diagram of a subprocess of step 114 of FIG. 4. Itillustrates an exemplary process by which a computer may update thecurrent price vector. FIG. 8 begins with step 114-1, in which an itemtype k not yet considered is selected. In step 114-2, a computercalculates the excess demand, denoted Z_(k), for item type k:$Z_{k} = {{- {\overset{\_}{Q}}_{k}} + {\sum\limits_{i = 1}^{n}\quad {Q_{k}^{i}.}}}$

[0090] The excess demand, Z_(k), has the interpretation of being theamount by which bidders in aggregate are bidding for quantities of itemtype k, in excess of the available quantity. The process then goes tostep 114-3, where the k^(th) component of the price vector is revisedby:

P _(k) ^(t+1) =P _(k) ^(t) +C _(k) Z _(k).

[0091] C_(k) is any arbitrary positive constant. Thus, the price foritem type k is raised if bidders bid for more than the availablequantity, and the price for item type k is reduced if bidders bid forless than the available quantity. The process then continues to step114-4, where it is determined whether all item types k have beenconsidered. If not, the process loops back to step 114-1. However, ifall item types k have already been considered, then updated prices forall item types have been generated, and the process proceeds to step 116of FIG. 4.

[0092] Embodiments Concerned with Intra-round Bids

[0093] In many of the leading dynamic electronic auctions in the priorart, bidders submit bids in a sequence of discrete rounds. For example,in the Federal Communications Commission auctions for radiocommunications spectrum or in the recent UMTS auctions held by Europeannations, the following would be a typical bidding schedule for anauction:

[0094] Round 1: 9:00-9:45

[0095] Round 2: 10:00-10:45

[0096] Round 3: 11:00-11:45

[0097] Round 4: 12:00-12:45

[0098] Round 5: 13:00-13:45

[0099] Round 6: 14:00-14:45

[0100] Round 7: 15:00-15:45

[0101] Round 8: 16:00-16:45

[0102] This bidding schedule would have the following interpretation.During the specified time period of each round, a bidder would berequired to submit a new bid or new collection of bids (unless thisbidder was already the standing high bidder on an item after the biddingof the previous round). If a bidder who was required to submit a new bidfailed to submit a new bid, then (except for provisions in the rulesconcerning automatic waivers) the bidder would be eliminated from theauction.

[0103] By contrast, some other electronic auctions in the prior art—forexample, online auctions at eBay—allow bidding to occur continuously.Rather than adhering to any rigid round schedule, bidders may submitbids at any times that they like up to a specified closing time. Relatedto this, there is no sense that a bidder is required to bid a certainamount by any particular time in order to retain eligibility to bid at alater time in the auction.

[0104] Many or most electronic auctions for high-valued items utilize adiscrete round structure, rather than allowing bidding to occurcontinuously. There appear to be several reasons for this. First, adiscrete round structure has desirable information properties. Theauction can be easily structured so that the results of Round t aredisseminated to bidders before the bids of Round t+1 need to besubmitted. Second, a discrete round structure is especially conducive toenforcing “activity rules,” in which a bidder is required to be active(i.e., either be the standing high bidder or place a new high bid) on agiven number of items in an earlier round of the auction in order tocontinue to bid on a given number of items in a later round of theauction. This forces bidders to effectively disclose to their opponents(through their bidding) the values that they attach to the items,helping to mitigate the well-known “Winner's Curse” present in auctions.Third, a discrete round structure requires a bidder to repeatedlyaffirm, in successive rounds, his willingness to pay a given price foran item in the auction—which may be especially desirable when items suchas communications licenses may sell for millions or billions of dollarsor euros.

[0105] At the same time, the desirable properties of a discrete roundstructure may come at some considerable cost. It will typically bereasonable to hold only something like 8 to 12 rounds of bidding in agiven day. As a result, the auctioneer must accept at least one ofseveral problems:

[0106] (1) The auction may be required to last a very long time: in someNorth American and European spectrum auctions, the bidding extended morethan 20 business days. Such a lengthy auction may be rather onerous forbidders and for the seller. In particular, it may discourage bidderparticipation, causing the seller to forgo substantial revenues.

[0107] (2) The bid increment between successive rounds may be requiredto be rather substantial: in some North American and European spectrumauctions, the bid increment between successive rounds never was allowedto drop below five percent of the previous bid. It can be argued that aseller suffers an expected revenue loss which is directly proportionalto the minimum bid increment, so this may cost a seller millions ofdollars or euros.

[0108] (3) The starting price may be required to be very near to theexpected closing price. This may discourage bidder participation, aswell as potentially eliminating the possibility of bidders gettingcaught up in the excitement of the auction and bidding very high prices(which is one of the advantages of conducting a dynamic auction). Thisalso runs the risk that the auction will fail: that is, quantities bidat the starting price being less than the available quantity at theauction. Moreover, in a clock auction, problem (2) above, a large bidincrement, may lead to a heightened risk of “undersell”. Consider anauction with an available quantity of 100 units of an item, and supposea bid increment of five percent. It is quite plausible that, at a priceof $1,000,000 per unit, the aggregate quantity bid by all bidders wouldequal 110 units, but at the next price of $1,050,000 per unit, theaggregate quantity bid by all bidders would decline to only 60 units.The auctioneer then faces the unattractive alternatives of: selling only60 units out of the available quantity of 100 units at a price of$1,050,000 each; rationing bidders so that only 100 units, out of the110 demanded, are sold at $1,000,000; or restarting the auction at$1,000,000. Observe however that the “undersell” problem would in alllikelihood have been substantially avoided, had a much smaller bidincrement been possible.

[0109] One embodiment of the present invention is a system and methodfor “Intra-Round Bids.” A discrete round structure—with all of its manyadvantages—is preserved. However, in Round t+1 of the auction, theauction system and method permits bidders to submit bids at pricesbetween the price associated with Round t and the price associated withRound t+1. Bidders have every incentive to utilize Intra-Round Bids, andto the extent that bidders utilize them, the seller should be expectedto attain higher auction revenues and to reduce the probability ofundersell. Thus, a system and method for Intra-Round Bids improves uponthe prior art for auction systems and methods, and has immediatepractical application for dynamic auctions of radio communicationsspectrum, securities and other financial products, electric power, etc.

[0110] While the previous and following description of Intra-Round Bidsis framed largely in terms of regular auctions to sell (where biddersare buyers), the invention is equally applicable for reverse orprocurement auctions to buy (where bidders are sellers). For the sake ofbrevity, this specification will not run through the process a secondtime with the roles of selling and buying reversed, but it should beclear to anybody skilled in the art that the technology can be equallyused in both situations.

[0111] Here is an example illustrating the usefulness and exact meaningof Intra-Round Bids. Suppose that, in a clock auction with an availablequantity of 100 units, the (end) price per unit associated with Round 4is $1,000,000, and the (end) price per unit associated with Round 5 is$1,050,000. In an auction with discrete bidding rounds, Bidder 1 mightsubmit a bid quantity of 55 units for Round 4 and a bid quantity of 30units for Round 5. If there also exists a Bidder 2 who submits the samebid quantities, then we would have exactly the “undersell” problemdescribed above: an aggregate quantity bid by all bidders of 110 unitsin Round 4 but only 60 units in Round 5 (with available quantity of 100units).

[0112] With an auction system and method for Intra-Round Bids, here isan example of the bids that Bidder 1 might submit for Auction Round 5:

[0113] 53 units at $1,010,000 per unit;

[0114] 51 units at $1,020,000 per unit;

[0115] 49 units at $1,030,000 per unit;

[0116] 45 units at $1,035,000 per unit;

[0117] 40 units at $1,040,000 per unit; and

[0118] 30 units at $1,045,000 per unit.

[0119] These bids have the following exact meaning: the parameterscorresponding to price indicate the price at which Bidder 1 wishes tochange his quantity demanded as compared to his “previous” (that is,next lower price) bid. Thus, in this example:

[0120] Bidder 1 is willing to purchase 55 units (his previous bid fromRound 4) at prices of $1,000,001-$1,009,999;

[0121] Bidder 1 is willing to purchase 53 units at prices of$1,010,000-$1,019,999;

[0122] Bidder 1 is willing to purchase 51 units at prices of$1,020,000-$1,029,999;

[0123] Bidder 1 is willing to purchase 49 units at prices of$1,030,000-$1,034,999;

[0124] Bidder 1 is willing to purchase 45 units at prices of$1,035,000-$1,039,999;

[0125] Bidder 1 is willing to purchase 40 units at prices of$1,040,000-$1,044,999; and

[0126] Bidder 1 is willing to purchase 30 units at prices of$1,045,000-$1,049,999.

[0127] If there also exists a Bidder 2 who submits the same bidquantities, then the auctioneer would be able to declare the auctionover at a price between $1,030,000 and $1,034,999, with 98 out of the100 available units sold. The auction revenues are improved, and theundersell problem is greatly reduced.

[0128]FIG. 9a is a flow diagram of a subprocess of step 106 of FIG. 4.It illustrates an exemplary process by which a particular bidder i maysubmit Intra-Round Bids. FIG. 9a begins with step 106-1, in which bidderi selects a group, G, of item types on which he wishes to place a bid. Gis a nonempty subset of {1, . . . , m}, the set of all item types. Instep 106-2, bidder i selects price parameters for group G representing aprice vector between the previous round's price vector for group G andthe current round's price vector for group G. In step 106-3, bidder iselects quantities of the item types of group G that he would like totake effect as bids at the selected price parameters. In step 106-4,bidder i expresses whether he wishes to enter more bids. If so, theprocess loops back to step 106-1. If not, the process continues to step106-5. In step 106-5, the computer determines whether bidder i hassubmitted at least one bid for each group G of item types. If not, theprocess loops back to step 106-1, and optionally the computer promptsbidder i to submit bids on the groups G of item types on which bidder ihas not submitted at least one valid bid in the current round. If so,the process goes to step 108 of FIG. 4.

[0129]FIG. 9b is a flow diagram of a subprocess of step 112 of FIG. 4.It illustrates an exemplary process by which a computer determineswhether the auction should continue, in a system where bidders arepermitted to submit Intra-Round Bids. FIG. 9b begins with step 112 b-1,in which a group G of item types not yet considered is selected. G is anonempty subset of {1, . . . , m}, the set of all item types. In step112 b-2, a computer sorts all bids entered for group G in the currentround. The sorting is done: first, by bidder ID; second, by priceparameter in the entered bid (in descending order); and third, by timestamp of submission (in descending order). In step 112 b-3, a computerselects, for each bidder i, the bid, Q_(G) ^(I), for group G with thehighest price parameter (and then the latest time stamp). In step 112b-4, a computer determines whether the aggregate quantity bid for groupG is no greater than the available quantity, that is, whether:${\sum\limits_{i = 1}^{n}\quad {\sum\limits_{k \in G}Q_{k}^{i}}} \leq {{\overset{\_}{Q}}_{G}.}$

[0130] If this inequality is not satisfied, then group G of item typeshas not yet cleared, and so the auction should continue. The processthus jumps immediately to step 114 of FIG. 4.

[0131] If the inequality of step 112 b-4 is satisfied, the process thengoes to step 112 b-5, where it is determined whether all groups G ofitem types have been considered. If not, the process loops back to step112 b-1. However, if all groups G of item types have already beenconsidered, then it has been found that all groups G of item types havecleared, and so the auction should not continue. The process proceeds tostep 118 of FIG. 4, where the final message is generated.

[0132]FIG. 9c is a flow diagram of a subprocess of step 118 of FIG. 4.It illustrates an exemplary process by which a computer determines finalallocations and payments, in a system where bidders are permitted tosubmit Intra-Round Bids. FIG. 9c begins with step 118 b-1, in which foreach bid entered in the current round, a computer expresses the priceparameter as a percentage of the distance from the previous round'sprice vector to the current round's price vector. For example, in theexample discussed above, where the (end) price per unit associated withRound 4 was $1,000,000, and the (end) price per unit associated withRound 5 was $1,050,000, a bid with a price parameter corresponding to$1,020,000 would imply a percentage distance parameter of 40%. In step118 b-2, a computer sorts the percentage distance parameters fromsmallest to largest, and denotes them π₁ <π₂< . . . <π_(N). In step 118b-3, a computer initializes the percentage distance parameter underconsideration, denoted π, to be the smallest value, π₁. In step 118 b-4,a group G of item types not yet considered is selected. In step 118 b-5,a computer sorts all bids entered for group G in the current round. Thesorting is done: first, by bidder ID; second, by percentage distanceparameter in the entered bid (in descending order); and third, by timestamp of submission (in descending order). In step 118 b-6, a computerselects, for each bidder i, the bid, Q_(G) ^(I), for group G with thehighest percentage distance parameter that is less than or equal to π(and then the latest time stamp). In step 118 b-7, a computer determineswhether the aggregate quantity bid for group G is no greater than theavailable quantity, that is, whether:${\sum\limits_{i = 1}^{n}{\sum\limits_{k \in G}Q_{k}^{i}}} \leq {{\overset{\_}{Q}}_{G}.}$

[0133] If this inequality is not satisfied, then group G of item typeshas not yet cleared at percentage distance parameter π, and so π needsto be incremented. The process thus goes to step 118 b-9, where π isadvanced to the next percentage distance parameter among π₁<π₂< . . .<π_(N). The process then loops back to step 118 b-4, using the newhigher value for π and starting over for groups G of item types.

[0134] If the inequality of step 118 b-7 is satisfied, the processcontinues to step 118 b-8, where it is determined whether all groups Gof item types have been considered. If not, the process loops back tostep 118 b-4. However, if all groups G of item types have already beenconsidered, then it has been found that all groups G of item types havecleared at percentage distance parameter π. Thus, the percentagedistance parameter π implies market-clearing prices for the auction. Theprocess proceeds to calculate the price vector implied by percentagedistance parameter π, to note the quantities bid by all bidders at thisprice vector, and to incorporate these computations into a final messagethat is outputted from a machine.

[0135] Observe that if the system and method for a dynamic clock auctionwith Intra-Round Bids is operated—but if the payment-account-calculationindicator of FIG. 5 is fixed at 0—this yields an embodiment of thepresent invention where bidders' payments are simply the dot products oftheir final bid vectors and the final price vector. Thus, the presentinvention also provides a fast and effective way to run a dynamic clockauction with a discrete round structure and uniform prices, practicaluse of the present invention.

1. A computer implemented method for auctioning at least two types ofitems, each of the types of items including plural items, the methodcomprising: a) communicating a price vector, including a price for eachof the types of items subject to the auction, to a plurality of bidders,b) receiving, in a computer, bids from plural bidders wherein at leastsome of said bids identify quantities of items of different types, c)determining, based on the received bids, whether the auction shouldcontinue, and in the event that the auction will continue, d) sending toone or more bidders a revised price vector, e) receiving, in thecomputer, further bids from plural bidders in response to the revisedprice vector and, in response to the further bids, f) crediting at leastone item of a particular type with a particular bidder at a price in aclosed interval between the price contained in the price vector and theprice contained in the revised price vector.
 2. A method as recited inclaim 1 wherein at least two different types of items are related toeach other.
 3. A method as recited in claim 1 wherein each type of itemis related to at least one different type of item.
 4. A method asrecited in claim 1 where the price in the closed interval is the pricecontained in the revised price vector.
 5. A method as recited in claim 1wherein the price in the closed interval is the price in the pricevector.
 6. A method as recited in claim 1 wherein at least one item ofeach selected type is credited to a bidder where a type is selected ifthe cumulative sum of quantities of that type has decreased in bids by asubset of bidders including all bidders except the bidder to becredited.
 7. A method as recited in claim 1 wherein the crediting to abidder occurs when at least one of those items, the bids for whichexhibited, in the bids of bidders other than the bidder, a cumulativedecrease in the further bids relative to the bids.
 8. A method asrecited in claim 1 wherein each type of item is the subject of a creditwhere, for that item, the bids exhibited, in the bids of bidders otherthan the bidder to be credited, a cumulative decrease in the furtherbids relative to the bids.
 9. A method as recited in claim 1 in which afurther bid from a bidder is limited so that the sum of the number ofitems contained in a bid is less than or equal to the sum of the numberof items contained in a bid submitted in the past.
 10. A method asrecited in claim 9 wherein the limitation is applied to a group, lessthan all, of the types of items.
 11. A method as recited in claim 1 inwhich a further bid from a bidder is limited so that the number of itemsof any type contained in a bid is less than or equal to the number ofthose items contained in a bid submitted in the past.
 12. A computerimplemented method for auctioning at least two types of items, each ofthe types of items including plural items, the method comprising: a)communicating a price vector, including a price for each of the types ofitems subject to the auction, to a plurality of bidders, b) receiving,in a computer, bids from plural bidders wherein at least some of saidbids identify quantities of items of different types, c) determining,based on the received bids, whether the auction should continue, and inthe event that the auction will continue, d) sending to one or morebidders a revised price vector, e) receiving, in the computer, furtherbids from plural bidders in response to the revised price vector and, inresponse to the further bids, f) selecting a particular bidder anddetermining, for a selected one of the types of items, whether the sumof the bids of other bidders is different in the further bids than inthe received bids, and if it is, crediting the bidder with a number ofthe selected type of items equal to the change in the sum of the bids ofother bidders at a price in a closed interval between the pricecontained in the price vector and the price contained in the revisedprice vector.
 13. A method as recited in claim 12 wherein thedetermination is effected for all other types of items.
 14. A method asrecited in claim 13 wherein the determination is effected for all otherbidders.
 15. A method as recited in claim 12 wherein the determinationis repeatedly effected on receipt of bids subsequent to the furtherbids.
 16. A method as recited in claim 12 wherein the price in theclosed interval is the price contained in the revised vector.
 17. Amethod as recited in claim 12 wherein the price in the closed intervalis the price contained in the price vector.
 18. A computer implementedmethod for auctioning at least two types of items, each type of theitems including plural items, the method comprising: a) communicating aprice vector, including a price for each of the types of items subjectto the auction, to a plurality of bidders, b) receiving, in a computersystem, bids from plural bidders wherein at least some of said bidsidentify quantities of items of different types, c) determining, basedon the received bids, whether the auction should continue, and in theevent that the auction will continue, d) sending to one or more biddersa revised price vector, e) receiving, in the computer system, furtherbids from plural bidders in response to the revised price vector and, inresponse to the further bids, [Is this what you intended?] f) crediting,to a bidder at least one of those items, the bids for which exhibited,in the bids of bidders other then the bidder, a cumulative decrease inthe further bids relative to the bids.
 19. A method as recited in claim18 wherein the credit is at a price in a closed interval between theprice contained in the price vector and the price contained in therevised price vector.
 20. A method as recited in claim 18 wherein atleast two different types of items are related to each other.
 21. Amethod as recited in claim 18 wherein each type of item is related to atleast one different type of item.
 22. A method as recited in claim 19where the price in the closed interval is the price contained in therevised price vector.
 23. A method as recited in claim 19 wherein theprice in the closed interval is the price in the price vector.
 24. Acomputer implemented method for auctioning at least two types of items,each of the types of items including plural items, the methodcomprising: a) communicating a price vector, including a price for eachof the types of items subject to the auction, to a plurality of bidders,b) receiving, in a computer system, bids from plural bidders wherein atleast some of said bids identify quantities of different types of items,c) determining, based on the received bids, whether the auction shouldcontinue, and in the event that the auction will continue d) sending toone or more bidders a revised price vector, e) receiving, in thecomputer system, further bids from plural bidders in response to therevised price vector and, in response to the further bids, f) crediting,to a selected bidder at least one of those items, the bids for whichexhibited, in bids of bidders other than the selected bidder, acumulative decrease in the further bids relative to the bids toestablish an item credit, and g) reducing the item credit in the eventbids, by bidders other than the selected bidder, show a cumulativeincrease in bids for that item after the item credit is established. 25.A method as recited in claim 24 wherein the credit is at a price in aclosed interval between the price contained in the price vector and theprice contained in the revised price vector.
 26. A method as recited inclaim 24 wherein at least two different types of items are related toeach other.
 27. A method as recited in claim 24 wherein each type ofitem is related to at least one different type of item.
 28. A method asrecited in claim 25 where the price in the closed interval is the pricecontained in the revised price vector.
 29. A method as recited in claim25 wherein the price in the closed interval is the price in the pricevector.
 30. A computer implemented method for auctioning at least twotypes of items, each type of the items including plural items, themethod comprising: a) communicating a price vector, including a pricefor each of the types of items subject to the auction, to a plurality ofbidders, b) receiving, in a computer system, bids from plural bidderswherein at least some of said bids identify quantities of items ofdifferent types, c) determining, based on the received bids, whether theauction should continue, and in the event that the auction will continued) sending to one or more bidders a revised price vector, e) limitingany further bid from a bidder so that the sum of the number of itemscontained in a bid is less than or equal to the sum of the number ofitems contained in a bid submitted in the past.
 31. A method as recitedin claim 30 wherein the bid is limited so the sum of the number of itemsof different types is less than or equal to the sum of the number ofitems of different types contained in a bid submitted in the past Islimited to the items from a group of types of items, where the group oftypes of items is less than all types of items.
 32. A method as recitedin claim 30 wherein the bid is limited so the number of items which isless than or equal to the number of items contained in a bid submittedin the past is items from a single type of the items.
 33. A method asrecited in claim 30 wherein the bid is limited so the number of itemswhich is less than or equal to the number of items contained in a bidsubmitted in the past applied separately to items from each type of theitems.
 34. A method as recited in claim 30 wherein the limiting isimplemented by rejecting any bid in which the sum of the number of itemscontained in the bid is not less than or equal to the sum of the numberof items contained in a bid submitted in the past.
 35. A method asrecited in claim 34 wherein bidders use terminals to manifest a bid andthe terminal rejects any bid in which the sum of the number of itemscontained in the bid is not less than or equal to the sum of the numberof items contained in a bid submitted in the past.
 36. A method asrecited in claim 30 which includes the further step of informing abidder that a bid has been rejected as not limited so that the sum ofthe number of items contained in a bid is less than or equal to the sumof the number of items contained in a bid submitted in the past.
 37. Amethod as recited in claim 36 wherein rejected bids are ignored in anydeterminations subsequent to the rejection.
 38. A method as recited inclaim 34 wherein the computer system rejects any bid in which the sum ofthe number of items contained in the bid is not less than or equal tothe sum of the number of items contained in a bid submitted in the past.39. A method as recited in claim 38 which includes the further step ofinforming a bidder that a bid has been rejected as not limited so thatthe sum of the number of items contained in a bid is less than or equalto the sum of the number of items contained in a bid submitted in thepast.
 40. A method as recited in claim 39 wherein rejected bids areignored in any determinations subsequent to the rejection.
 41. Acomputer implemented method useful in applying a constraint in a clockauction, comprising the steps of: Conveying information, includingprices for two or more types of items, to at least one bidder, Receivingfrom said bidder, information for a bid comprising quantities for saidtypes of items, and Applying a constraint to the bid information torequire that the sum of the quantities over a group of item types is nolarger than the sum of quantities over a group of item types containedin a prior bid.
 42. A method as recited in claim 41 wherein the group ofitem types is less than all the item types subject to the auction.
 43. Amethod as recited in claim 41 wherein the group of item types includes asingle item type.
 44. A method as recited in claim 42 wherein the bidinformation is limited so that, for each different type of item, thenumber of items in a bid is no larger than the number of items containedin a prior bid.